If you want to sing an E over a C chord do that if you want to sing a Dflat over that same C you do so if you like how it sounds
Snging is like playing any other melody musoc wise sing the notes that give the desired effect

Start off by singing the notes in the chords. Most of the main notes that stand out singing are from the chords and if you get those right the other notes around that will come much easier and will be in tune.